![[Plouffe's Inverter]](figs/invertersmall.gif)
Table of current records for the
computation of constants
last update was June 8, 2000 by
Simon
Plouffe
-
- N'th binary digit
computations
- Other
records
- Notes
Classical
constants
- Pi =
3.141592653589...
- Precision : 206,158,430,000
decimal digits (almost 3*2^36).
- Time of computation : about 37 and 46 hours
for each computation.
- Machine: HITACHI
SR8000.
- Who : Yasumasa Kanada and Daisuke Takahashi
(University of Tokyo).
- When : From June 26 to September 20 1999 (2
independant runs).
- Algorithms : Gauss-Legendre and Borwein's 4'th
order iteration.
-
- 1/Pi =
0.3183098661...
- Precision : 206,158,430,000
digits which is almost 3*2^36.
- Time of computation:
Same as above
- When : From June 26 to September 20 1999 (2
independant runs).
- Algorithm : Gauss-Legendre and Borwein's 4'th
order iteration.
-
E =
2.71828182845...
- Precision : 1,250,000,000
digits.
(for downloads see The
Big files directory)
- Time of computation: real time: 79 hours and
30 minutes.
- Who : Xavier Gourdon
- When : 1999, Nov, 14 (verification : 1999, Nov 21)
- Timing : The computation took 39h and 52 minutes on a IBM
ThinkPad
- (PII 350 Mhz, 320 Mo of memory). The verification took 40
hours 25
- minutes on the same machine.
Catalan =
0.915965594...
- Precision : 12,500,000
digits. (for downloads see The
Big files directory)
- Machine: sgi r10000, 256 Mo of
memory.
- Time of computation: 18 hours, 1
min.
- Who : Xavier
Gourdon (Xavier.Gourdon@inria.fr)
- When : December 30-31, 1997.
Zeta(3) =
1.2020569031...
- Precision : 128,000,026
digits. (for downloads see The
Big files directory)
- Time of computation:
under 40 hours
- Machines :IBM S/390 G5 CMOS (9672-RX6) and IBM
Power2 SC 135 MHz, 2 GB RAM, GNU C++ 2.8.0, AIX 4.1.5. and IBM
PowerPC 604e 233 MHz, 1 GB RAM, GNU C++ 2.8.0, AIX
4.1.5.
- Who : Sebastian Wedeniwski (wedeniws@de.ibm.com)
- When : December 13, 1998
- Note : Agrees with double computation to 128
million digits.
-
Euler's gamma =
0.577215664901...
- Precision : 108,000,000
digits.
- Time of computation: 47 hours and 36
minutes.
- Machine: HP J5000, 2 processors PA 8500 (440
Mhz), 2 Gigabytes of memory.
- Who : Patrick Demichel and Xavier Gourdon see
also his constants
page.
- When : between September 23 and 26,
1999.
log(2) =
0.69314718055...
- Precision : 108,000,000
digits. (for downloads see The
Big files directory)
- Time of computation: 47 hours.
- Machine: sgi r10000, 256 Mo of
memory.
- Who : Xavier Gourdon : see also his
constants
page.
- When : from January 23 to 25, 1998
Golden Ratio = 1.6180339887...
and the square root of 5
-
- Precision : Over 1.5
billion digits. (for downloads see The
Big files directory for 10 million
digits).
- Time of computation: Less than 3 hours in
all.
- Machine: Pentium III, 700 Mhz, 512 Megabytes
RAM + 10 gigs disk.
- Who : Xavier Gourdon and Pascal Sebah see also
constants
page for other details.
- When : May 2000.
Square root of 2 =
1.414213562373095...
-
- Precision : 137,438,953,444 digits
(2^37-28).
- Time of computation: 7.5 hours and 205 Gb of
main memory.
- Machine : Hitachi SR2201 with 1024
processors.
- Who : Yasumasa Kanada and Daisuke Takahashi
.
- When : August 03, 1997.
N'th
binary digit computations of Pi
Bailey, Borwein, Plouffe Nov. 1995 40,000,000,000 (hexa 921C73C6838FB2)
Bellard Jul. 1996 200,000,000,000 (hexa 1A10A49B3E2B82A4404F9193AD4EB6)
Bellard Oct. 1996 400,000,000,000 (hexa 9C381872D27596F81D0E48B95A6C46)
Percival Jan, 1998 800,000,000,000 (hexa 3E6FBDAC38A97197785ED).
Bellard Sep. 1997 1,000,000,000,000 (hexa 87F72B1DC9786914B15B16FE9218B042A3D410 )
Pihex project August 21, 1998 5,000,000,000,000 (hexa 07E45733CC790B5B5979).
Pihex project February 9,1999 40,000,000,000,000 (hexa A0F9FF371D17593E0).
Pihex project To come 1000,000,000,000,000 almost done!
- Other
interesting computations
-
- Continued
Fraction expansion of Pi :
20,000,000 terms by Hans
Havermann (June 1999).
- Bernoulli
Numbers: B10000,
, B30000,
B72000,
B100000,
B200000
by Greg J. Fee and Simon Plouffe
- Zeros of Riemann's Zeta
Function, first
100 zeros to 1000
Digits by Andrew
M. Odlyzko.
- Madelung
Constant,
by David H. Bailey
(1995).
- Khintchine
Constant,
110,000 Digits by Xavier
Gourdon
- Zeta(3) and
Zeta(5) : by
David
Broadhurst :
40,000,000'th binary digit (1998).
- Zeta(5)
: David
Broadhurst and Patrick
Demichel : 1000000 digits (July 1998).
- Zeta(7)
: 50000 digits by Simon
Plouffe (July 23
1998).
- Zeta
values (from 3 to 99) by Robert
J. Harley to 10000 digits each (July 1998).
- Feigenbaum's
Constant : 578 digits (Keith Briggs and David H.
Bailey).
- Additional
notes.
-
- Pi in hexadecimal (or binary).
-
-
- The 5 trillion'th binary digit of Pi was computed twice and
the project was conducted by Colin Percival with the help of more
than 25 other people and their computers (mostly all Pentiums).
The computation took more than 13500 hours of combined CPU.
Details of the project are at Simon
Fraser University. Percival also initiated the computation of
the position 40*10^12 and also 10^15.
-
- Exp(1) : The computation of exp(1) was carried to 1.7
billion digits by Patrick Demichel before Nov. 21 1999 and was
used to verify Xavier Gourdon computation
-
Computation of sqrt(2)/2 was carried at the same time as
the one for sqrt(2) and took only 32.5 minutes to check.
-
If you think you can do better than any of those records : Yes, go
ahead, this is exactly why this page is
here. Send files/comments/suggestions to
plouffe@math.uqam.ca
-